LONDON (Reuters) - Deepening ties with European companies and "old friends" like the United States and Japan would help Britain preserve its global role in finance after leaving the EU, an industry body said on Wednesday.

TheCityUK published a to-do list for the financial sector and government, saying June's vote to leave the European Union magnified the challenge of keeping up with global competition in finance.

Frankfurt, Amsterdam, Paris and Milan all hope to win a slice of London's market share in financial services.

TheCityUK's chief executive Chris Cummings said Britain must make more of how much companies across Europe rely on Britain's financial services and allied professions like accounting and law to do business.

The backing of these companies would be important in upcoming UK-EU trade talks to ensure continued access to the single market.

"What I hear from major European corporates is they like to do business through London due to the depth of the talent pool and capital markets here," Cummings said.

As major "buyers" of financial services still want to come to London, the "sellers" such as banks are staying put, he added.

"We are talking about mutual market access. France or Germany could build deeper pools of capital, but that could not happen quickly."

In its report, the industry body called on the finance ministry to strengthen its Financial Services Trade and Investment Board.

Its work should also focus as much on "old friends" like the United States and Japan as on new markets in China and India.

Britain's new trading terms with the EU may not be known for several years.

"We must now speak confidently and with one voice to policymakers to help inform them about the deal we want to see from the upcoming negotiations," TheCityUK Chairman John McFarlane said.

In the meantime, it was crucial that the government drums home the message that Britain is a stable place to do business.

Cummings said it was realistic that Britain's new Prime Minister Theresa May wanted to review a major project like the Hinkley Point nuclear power plant, a move that has taken China, one of its backers, by surprise.

But it was important that Britain remains open to business, and that the prime minister and her team continue to build a constructive relationship with European leaders, Cummings said.